The factorization method for inverse problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford lecture series in mathematics and its applications
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 201 S. graph. Darst. |
| ISBN: | 0199213534 9780199213535 |
Internformat
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| 100 | 1 | |a Kirsch, Andreas |d 1953- |e Verfasser |0 (DE-588)121174328 |4 aut | |
| 245 | 1 | 0 | |a The factorization method for inverse problems |c Andreas Kirsch and Natalia Grinberg |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XIV, 201 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Oxford lecture series in mathematics and its applications |v 36 | |
| 650 | 4 | |a Inverse problems (Differential equations) | |
| 650 | 4 | |a Factorization (Mathematics) | |
| 650 | 0 | 7 | |a Faktorisierung |0 (DE-588)4128927-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inverses Problem |0 (DE-588)4125161-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4006432-3 |a Bibliografie |2 gnd-content | |
| 689 | 0 | 0 | |a Inverses Problem |0 (DE-588)4125161-1 |D s |
| 689 | 0 | 1 | |a Faktorisierung |0 (DE-588)4128927-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Grinberg, Natalia |e Sonstige |0 (DE-588)120050927 |4 oth | |
| 830 | 0 | |a Oxford lecture series in mathematics and its applications |v 36 |w (DE-604)BV009910017 |9 36 | |
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Datensatz im Suchindex
| _version_ | 1804137514876796928 |
|---|---|
| adam_text | Contents
Preface
v
1
The simplest cases: Dirichlet and Neumann boundary conditions
1
1.1
The Helmholtz equation in acoustics
2
1.2
The direct scattering problem
4
1.3
The far field patterns and the inverse problem
7
1.4
Factorization methods
13
1.4.1
Factorization of the far field operator
15
1.4.2
The inf-criterion
19
1.4.3
The (F*^) ^-method
22
1.5
An explicit example
29
1.6
The Neumann boundary condition
31
1.7
Additional remarks and numerical examples
35
2
The factorization method for other types of inverse obstacle scattering
problems
40
2.1
The direct scattering problem with impedance boundary conditions
40
2.2
The obstacle reconstruction by the inf-criterion
49
2.3
Reconstruction from limited data
52
2.4
Reconstruction from near field data
54
2.5
The F#
-
factorization method
57
2.5.1
The functional analytic background
57
2.5.2
Applications to some inverse scattering problems
62
2.6
Obstacle scattering in a half-space
63
2.6.1
The direct scattering problem
65
2.6.2
The factorization method for the inverse problem
67
3
The mixed boundary value problem
70
3.1
The direct scattering problem
70
3.2
Factorization of the far field operator
76
3.3
Application of the F#- factorization method
79
4
The MUSIC algorithm and scattering by an inhomogeneous medium
86
4.1
The MUSIC algorithm
86
4.2
Scattering by an inhomogeneous medium
91
4.3
Factorization of the far field operators
95
4.4
Localization of the support of the contrast
97
4.5
The interior transmission eigenvalue problem
102
xiv Contents
5
The factorization method for Maxwell s equations
109
5.1
Maxwell s equations
109
5.2
The direct scattering problem
111
5.3
Factorization of the far field operator
123
5.4
Localization of the support of the contrast
125
5.5
The interior transmission eigenvalue problem
133
6
The factorization method in impedance tomography
141
6.1
Derivation of the models
141
6.2
The Neumann-to-Dirichlet operator and the inverse problem
142
6.3
Factorization of the Neumann-to-Dirichlet operator
148
6.4
Characterization of the inclusion
150
7
Alternative sampling and probe methods
159
7.1
Two approximation results
159
7.2
The dual space method and the linear sampling method
163
7.3
The singular sources method
171
7.4
The probe method
176
7.4.1
The probe method in impedance tomography
176
7.4.2
The probe method for the inverse scattering problem with mixed
boundary conditions
183
Bibliography
189
Index
199
|
| adam_txt |
Contents
Preface
v
1
The simplest cases: Dirichlet and Neumann boundary conditions
1
1.1
The Helmholtz equation in acoustics
2
1.2
The direct scattering problem
4
1.3
The far field patterns and the inverse problem
7
1.4
Factorization methods
13
1.4.1
Factorization of the far field operator
15
1.4.2
The inf-criterion
19
1.4.3
The (F*^) ^-method
22
1.5
An explicit example
29
1.6
The Neumann boundary condition
31
1.7
Additional remarks and numerical examples
35
2
The factorization method for other types of inverse obstacle scattering
problems
40
2.1
The direct scattering problem with impedance boundary conditions
40
2.2
The obstacle reconstruction by the inf-criterion
49
2.3
Reconstruction from limited data
52
2.4
Reconstruction from near field data
54
2.5
The F#
-
factorization method
57
2.5.1
The functional analytic background
57
2.5.2
Applications to some inverse scattering problems
62
2.6
Obstacle scattering in a half-space
63
2.6.1
The direct scattering problem
65
2.6.2
The factorization method for the inverse problem
67
3
The mixed boundary value problem
70
3.1
The direct scattering problem
70
3.2
Factorization of the far field operator
76
3.3
Application of the F#- factorization method
79
4
The MUSIC algorithm and scattering by an inhomogeneous medium
86
4.1
The MUSIC algorithm
86
4.2
Scattering by an inhomogeneous medium
91
4.3
Factorization of the far field operators
95
4.4
Localization of the support of the contrast
97
4.5
The interior transmission eigenvalue problem
102
xiv Contents
5
The factorization method for Maxwell's equations
109
5.1
Maxwell's equations
109
5.2
The direct scattering problem
111
5.3
Factorization of the far field operator
123
5.4
Localization of the support of the contrast
125
5.5
The interior transmission eigenvalue problem
133
6
The factorization method in impedance tomography
141
6.1
Derivation of the models
141
6.2
The Neumann-to-Dirichlet operator and the inverse problem
142
6.3
Factorization of the Neumann-to-Dirichlet operator
148
6.4
Characterization of the inclusion
150
7
Alternative sampling and probe methods
159
7.1
Two approximation results
159
7.2
The dual space method and the linear sampling method
163
7.3
The singular sources method
171
7.4
The probe method
176
7.4.1
The probe method in impedance tomography
176
7.4.2
The probe method for the inverse scattering problem with mixed
boundary conditions
183
Bibliography
189
Index
199 |
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| author | Kirsch, Andreas 1953- |
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| ctrlnum | (OCoLC)166387314 (DE-599)HBZHT015367700 |
| dewey-full | 515.35 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
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| illustrated | Illustrated |
| index_date | 2024-07-02T20:17:42Z |
| indexdate | 2024-07-09T21:13:31Z |
| institution | BVB |
| isbn | 0199213534 9780199213535 |
| language | English |
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| publisher | Oxford Univ. Press |
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| series | Oxford lecture series in mathematics and its applications |
| series2 | Oxford lecture series in mathematics and its applications |
| spelling | Kirsch, Andreas 1953- Verfasser (DE-588)121174328 aut The factorization method for inverse problems Andreas Kirsch and Natalia Grinberg 1. publ. Oxford [u.a.] Oxford Univ. Press 2008 XIV, 201 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford lecture series in mathematics and its applications 36 Inverse problems (Differential equations) Factorization (Mathematics) Faktorisierung (DE-588)4128927-4 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf (DE-588)4006432-3 Bibliografie gnd-content Inverses Problem (DE-588)4125161-1 s Faktorisierung (DE-588)4128927-4 s DE-604 Grinberg, Natalia Sonstige (DE-588)120050927 oth Oxford lecture series in mathematics and its applications 36 (DE-604)BV009910017 36 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016411094&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kirsch, Andreas 1953- The factorization method for inverse problems Oxford lecture series in mathematics and its applications Inverse problems (Differential equations) Factorization (Mathematics) Faktorisierung (DE-588)4128927-4 gnd Inverses Problem (DE-588)4125161-1 gnd |
| subject_GND | (DE-588)4128927-4 (DE-588)4125161-1 (DE-588)4006432-3 |
| title | The factorization method for inverse problems |
| title_auth | The factorization method for inverse problems |
| title_exact_search | The factorization method for inverse problems |
| title_exact_search_txtP | The factorization method for inverse problems |
| title_full | The factorization method for inverse problems Andreas Kirsch and Natalia Grinberg |
| title_fullStr | The factorization method for inverse problems Andreas Kirsch and Natalia Grinberg |
| title_full_unstemmed | The factorization method for inverse problems Andreas Kirsch and Natalia Grinberg |
| title_short | The factorization method for inverse problems |
| title_sort | the factorization method for inverse problems |
| topic | Inverse problems (Differential equations) Factorization (Mathematics) Faktorisierung (DE-588)4128927-4 gnd Inverses Problem (DE-588)4125161-1 gnd |
| topic_facet | Inverse problems (Differential equations) Factorization (Mathematics) Faktorisierung Inverses Problem Bibliografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016411094&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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